My understanding was that the CEV approach is a meta-level approach to stable self improvement, aiming to design code that outputs what we would want an FAI's code to look like (or something like this). I could certainly be wrong of course, and I have very little to go on here, as the Knowability of FAI and CEV are both more vague than I would like (since, of course, the problems are still way open) and several years old, so I have to piece the picture together indirectly.

If that interpretation is correct it seems (and I stress that I might be totally off base with this) that stable recursive self-improvement over time is not the biggest conceptual concern, but rather the biggest conceptual difficulty is determining how to derive a coherent goal set from a bunch of Bayesian utility maximizers equipped with each individual person's utility function (and how to extract each person's utility function), or something like that. A stable self-improving code would then (hopefully) be extrapolated by the resulting CEV, which is actually the initial dynamic.